5 Exam-style ABCD is a kite.
The coordinates of A are (−1, 3).
The equation of the diagonal BD is y = 3x − 1.
Find the equation of the diagonal AC.
let's recall that in a Kite the diagonals meet each other at 90° angles, Check the picture below, so we're looking for the equation of a line that's perpendicular to BD and that passes through (-1 , 3).
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of BD
\(y = \stackrel{\stackrel{m}{\downarrow }}{3}x-1\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)
\(\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{3\implies \cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}\)
so we're really looking for the equation of a line whose slope is -1/3 and passes through point A
\((\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{1}{3}}[x-\stackrel{x_1}{(-1)}]\implies y-3=-\cfrac{1}{3}(x+1) \\\\\\ y-3=-\cfrac{1}{3}x-\cfrac{1}{3}\implies y=-\cfrac{1}{3}x-\cfrac{1}{3}+3\implies y=-\cfrac{1}{3}x+\cfrac{8}{3}\)
Will someone be able to help me with this math problem, the picture is down below. Please help
The dilation transformation of the triangle ABC by a scale factor of 3, with the point P as the center of dilation indicates;
Side A'B' will be parallel to side AB
Side A'C' will be parallel to side AC
Side BC will lie on the same line as side BC
What is a dilation transformation?A dilation transformation is one in which the dimensions of a geometric figure are changed but the shape of the figure is preserved.
The possible options, from a similar question on the internet are;
Be parallel to
Be perpendicular to
Lie on the same line as
The location of the point P, which is the center of dilation, and the lines PC and PA of dilation and the scale factor of dilation indicates that we get;
PB' = 3 × PB
PA' = 3 × PA
PC' = 3 × PC
Therefore; The side B'C' will be on the same line as the side BC
The Thales theorem, also known as the triangle proportionality theorem indicates that;
The side A'C' will be parallel to the side AC
The side A'B', will be parallel to the side AB
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9 cm
7 cm
7 cm
7 cm
The area of one of the bases of the above figure is about 21.2 cm2. The
surface area of the figure is?
A. 273.4 cm2
B. 210.4 cm2
C. 231.4 cm2
D. none of the above
Answer:
d
Step-by-step explanation:
none of the above mhhmm
Answer:
the answer to the question is 231.4 cm^2
Step-by-step explanation:
just got it wrong
Which ratio is equivalent to 4:10?
A:2/5
B.8/10
C:12/16
D:16/10
Answer: It d
Step-by-step explanation:
8 ft
10 ft
Find the perimeter of this figure to
the nearest hundredth.
Use 3.14 to approximate .
P = [?] ft
Notice that only half of the circle is included in the figure!
The perimeter of the figure is 4(π + 9)ft.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
Given is a 2 - D figure as shown in the figure attached.
We can write the perimeter as -
P = P{rectangle} + P{semicircle}
P = 2(10 + 8) + (4π)
P = (4π) + (36)
P = 4(π + 9)
Therefore, the perimeter of the figure is 4(π + 9)ft.
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The original cost of an item is $64 but you have to pay $78.08. What is the markup of the item as a percent
Answer:
22%
Step-by-step explanation:
$78.08 - $64 = $14.08
$14.08 * 100% / $64 = 22%
A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be 99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
The sample size needed to be 99% confident that the sample proportion will not differ from the true proportion by more than 4% is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
\(\pi = 0.5\)
Then the sample size for M = 0.04 is obtained as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)
\(0.04\sqrt{n} = 2.575 \times 0.5\)
\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)
\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)
n = 1037.
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What is the value of 2.7 x 4.1?
Answer:
11.07
Step-by-step explanation:
2.7
x4.1
=11.07
Answer:
11.07
Step-by-step explanation:
Select the choice that represents the two-variable
equation after it has been solved for x in terms of y.
2y - 3x = 0
The two variable equations when solved for x in terms of y is given as the equation y = 3x/2, and option A is the correct answer.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
The given equation is:
2y - 3x = 0
Add 3x on both sides of the equation:
2y -3x + 3x = 3x
2y = 3x
Divide both sides of the equation with 2:
2y / 2 = 3x / 2
y = 3x/2
Hence, the two variable equations when solved for x in terms of y is given as y = 3x/2, and option A is the correct answer.
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The correct question is:
I need a help with this hw
The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5 d ) -25/12
What is trigonometric ratio?
Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent. Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse
the give parameters are:
tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2
a) sin(α+β)
Using the trig ratios tan = opp/adj
but from pyth. rule, 4² + 3² = h²
16+9 = h²
h = √25 = 5
Now from trig Sin(α+β)
4/5 + 3/5
=- 7/5
b) cos(α+β)
cos = ad/hypo
4/5 + 3/5
= -7/5
c) Sin(α-β)
4/5 - 3/5
-1/5
d) tan(α-β)
= -4/3 - 3/4
= (-16 - 9)/ 12
-25/12
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HELP ASAP
The scale on a map shows that 2 inches represents 15 miles. Which proportion can be used to find the actual distance,
X, represented by 30 inches on the map?
2 30
15
2 X
1530
15
2
0 30
15 X
302
Answer:
The proportion that can be used is
2 inches 30 inches
15 miles x
Step-by-step explanation:
If 15 miles is 2 inches and 30 divided by 2 is 15, you have to multiply 15 by 15 to figure out how many miles 30 inches is. Because 15 x 15 = 225, 30 inches is 225 miles. Therefore, x = 225.
Find the value of x for the following
Answer:
x = 10
Step-by-step explanation:
The 2 angles shown are corresponding angles and therefore are congruent.
8x + 41 = 121
8x = 121 - 41 = 80
x = 80/8 = 10
Answer:
x = 10
Step-by-step explanation:
Given angles are,
→ 8x + 41°
→ 121°
Now we have to,
→ Find the required value of x.
We know that,
→ Corresponding angles are equal.
Forming the equation,
→ 8x + 41° = 121°
Then the value of x will be,
→ 8x + 41° = 121°
→ 8x = 121° - 41°
→ 8x = 80
→ x = 80 ÷ 8
→ [ x = 10 ]
Hence, the value of x is 10.
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be 95% confident that the sample mean is within 4 IQ points of the true mean.
What is the required sample size?
Answer:
55
Step-by-step explanation:
\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)
Make sure to always round up the required sample size to the nearest integer!
What is the approximate length of side GF in triangle EFG?
Answer:
41.93 degrees
Step-by-step explanation:
Determine the measure of the arc CED
Answer:kbef;eohrjkvoubwe
cv bojbDetectives are unsure whether Kendall Postwell will be able to testify at her trial. They say it is a question of competence. What does this MOST likely mean?
A.
Kendall might be determined to be insane and not qualified to testify.
B.
The evidence in Kendall’s case is inconclusive and doesn’t prove anything.
C.
Kendall is an expert witness who has testified many times before.
D.
The police think it will hurt their case if Kendall chooses to testify.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Arc length= \(\frac{interior angle}{360} 2\pi r\)
What values of b satisfy 3(2b + 3)² = 36?
Answer:
The values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
Step-by-step explanation:
To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:
1. Divide both sides of the equation by 3:
(2b + 3)² = 12
2. Take the square root of both sides:
√[(2b + 3)²] = √12
Simplifying further:
2b + 3 = ±√12
3. Subtract 3 from both sides:
2b = ±√12 - 3
4. Divide both sides by 2:
b = (±√12 - 3) / 2
Simplifying further:
b = (±√4 * √3 - 3) / 2
b = (±2√3 - 3) / 2
Therefore, the values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
Isreal spends the most time on social media with a total of 11.1.peru has a total of 8.3 how much more time does israel spend on social media
Answer:
2.8
Step-by-step explanation:
11.1-8.3=2.8
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
3 + y + y +y = 3+ y3
Answer:
\( {y}^{3} + 3\)
Step-by-step explanation:
Theory : A sum of two perfect cubes, a3 + b3 can be factored into :
(a+b) • (a2-ab+b2)
Proof : (a+b) • (a2-ab+b2) =
a3-a2b+ab2+ba2-b2a+b3 =
a3+(a2b-ba2)+(ab2-b2a)+b3=
a3+0+0+b3=
a3+b3
Check : 3 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Find a point on the curve x^3+y^3=11xy other than the origin at which the tangent line is horizontal.
(Use symbolic notation and fractions where needed. Give your answer as a point's coordinates in the form (* , *).)
Compute the derivative dy/dx using the power, product, and chain rules. Given
x³ + y³ = 11xy
differentiate both sides with respect to x to get
3x² + 3y² dy/dx = 11y + 11x dy/dx
Solve for dy/dx :
(3y² - 11x) dy/dx = 11y - 3x²
dy/dx = (11y - 3x²)/(3y² - 11x)
The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when
11y - 3x² = 0
or
y = 3/11 x²
(provided that 3y² - 11x ≠ 0)
Substitute y into into the original equation:
x³ + (3/11 x²)³ = 11x (3/11 x²)
x³ + (3/11)³ x⁶ = 3x³
(3/11)³ x⁶ - 2x³ = 0
x³ ((3/11)³ x³ - 2) = 0
One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with
(3/11)³ x³ - 2 = 0
(3/11 x)³ - 2 = 0
(3/11 x)³ = 2
3/11 x = ³√2
x = (11•³√2)/3
Solving for y gives
y = 3/11 x²
y = 3/11 ((11•³√2)/3)²
y = (11•³√4)/3
So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).
Identify the volume of a regular triangular pyramid with base edge length 14 ft and height 9 ft.
Answer:
The volume is 588 ft³
Step-by-step explanation:
\(v = a {}^{2} \frac{h}{3} = 14 {}^{2} \times \frac{9}{3} = 588\)
Answer:
254.6 ft3 F
Step-by-step explanation:
To find the volume of the pyramid, first calculate the area of the base.
As the pyramid is the regular triangular pyramid, the base is an equilateral triangle.
To find the area of the equilateral triangle, calculate the length of the height.
Since the triangle is equilateral, each angle in the triangle equals 60°.
The height forms a 30°- 60°- 90° triangle. One leg of this triangle is equal to half of the side of the large triangle, or 7 ft. The other leg of the triangle is equal to 73‾√ ft by the 30°- 60°- 90° Triangle Theorem.
Therefore, the length of the height of the triangle is 73‾√ ft.
To find the area of the base of the pyramid, B, use the formula for the area of a triangle, B=12bh.
Substitute 14 for b and 73‾√ for h.
B=12⋅14⋅73‾√
Simplify.
B=493‾√ ft2
To find the volume of the pyramid, use the formula for the volume of a pyramid, V=13Bh.
Substitute 493‾√ for B and 9 for h.
V=13⋅493‾√⋅9
Simplify.
V=1473‾√
Use a calculator to approximate.
V≈254.6 ft3
Therefore, the volume of the regular triangular pyramid is about 254.6 ft3.
A concrete plant uses the following proportions per m3 of concrete: cement 310 kg; water 180 kg; fine aggregate 750 kg and coarse aggregate 1080 kg both in SSD conditions. If the fine aggregate in the field has 4% excess water find the revised quantity of water. cehgg
Answer:
150 kg
Step-by-step explanation:
Given that
cement = 310 kg
Fine aggregate = 750 kg
coarse aggregate = 1080 kg
mass of water = 180 kg
given that aggregate in field is 4% excess water
Determine the revised quantity of water
mass of concrete per m^3 = mass of cement + mass of water + mass of fine aggregate + mass of coarse aggregate
therefore mass of concrete = 310 + 180 + 750 + 1080 = 2320 kg
given that fine aggregate in field has 4% excess water this simply means it was void of air in the concrete the new weight = (1.04 * 750) = 780
Hence the revised quantity of water ( x )
= 310 + x + 780 + 1080 = 2320
therefore x = 150 kg
I need help with both of these can someone please help me
After the shutdown, the hospital will maintain 126 acute hospital beds available for usage.
Which categories and what is a hospital?Hospitals are classified as general, specialist, or government facilities by the source of their funding. In a medical center, nursing education and patient care are both integrated. A care facility which is smaller than a hospital is called a clinic.
If 28% of the hospital's acute card beds are going to ever be closed, that leaves 100% - 28% = 72% of such beds available for utilization.
72% of 175 beds = 0.72 x 175 = 126 beds
As a result, following the shutdown, the hospital will still have 126 basic card beds available for usage.
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Answer fast please i got 10 min left
In rst cos r = 3/5 what is sin t
Answer:
sin 4/9 if cos is 3/5
Step-by-step explanation:
A cosine function is equivalent to the adjacent side divided by the hypotenuse , from SOH-CAH-TOA.
So, our adjacent side can be 3 , and the hypotenuse can be 5.
Then, we can use the Pythagorean theorem (a^2 + b^2 = c^2) to find the missing side length.
3^2+b^2=5^2
9+b^2 =25
b^2=16
b = 4
We found our three sides: 4, 5, and 9.
We know from SOH-CAH-TOA that the sine function is equivalent to the opposite side length divided by the hypotenuse length. So:
sin θ = 4/9
Look at the graph. On a coordinate plane, a graph increases through (negative 1, 4), levels off at (0, negative 3), and then increases up through (2, 5). Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be (–1, –4), (0, -3), and (2, 5). Next, she determined the rate of change between the points (–1, –4) and (0, -3) to be StartFraction negative 3 minus (negative 4) Over 0 minus (negative 1) EndFraction = StartFraction 1 Over 1 EndFraction = 1. and the rate of change between the points (0, -3) and (2, 5) to be StartFraction 5 minus (negative 3) Over 2 minus 0 EndFraction = StartFraction 8 Over 2 EndFraction = 4. Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong? The points (–1, –4), (0, –3), and (2, 5) are not all on the graph. The expressions StartFraction negative 3 minus (negative 4) Over 0 minus (negative 1) EndFraction and StartFraction negative 3 minus (negative 5) Over 2 minus 0 EndFraction both equal 1. She miscalculated the rates of change. Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.
Answer:
Answer is A
explanation:
there is no point (0.-3) on the graph.
Answer:
it's D edg 2020
Step-by-step explanation:
What is the length of ? A. 13 B. 9 C. 81 D. 11
Answer:
C. 81
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
AP3X
44 and 45 are alternate interior
angles. Find the measure of 25.
{
11565°
43/44
44 = 115°
45 = [?]
45/46
47/48
274
Answer:
115°
Step-by-step explanation:
angles 4 and 5 are alternate angles which means they would be the same amount
Answer:
Solution given:
<5=115°[corresponding angle]
3.3(x + 1.2) = 40.26
Answer: x=11
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
3.3(x + 1.2) = 40.26
Distribute the 3.3 across the parentheses.
3.3x + 3.96 = 40.26
Combine the constants by subtracting 3.96 from both sides
3.3x = 36.3
Isolate the variable by dividing both sides by 3.3
x = 11
Check your work by plugging x = 11 into the original equation.
3.3(11 + 1.2) = 40.26
3.3(12.2) = 40.26
40.26 = 40.26
Your answer is correct.
Hope this helps!
A ratio of two angles is 5 to 3 and their sum is 180 degrees. Find the measure of each angle. The find their complements. Make a sketch, set up the corresponding equation and solve it.
Answer:
112.5
67.5
Step-by-step explanation:
We know the ratio is:
5:3
So, we can write it as:
5x+3x=180, with 5x being one angle, and 3x being the other
combine like terms
8x=180
divide both sides by 8
x=22.5
5(22.5)=112.5
3(22.5)=67.5
So, one angle is 112.5 and the other is 67.5.
Hope this helps!
8b+3=35. when solving for B what is ur first step
Answer:
Put B on the one side, then the numbers go on the other side
Find the value of x
Answer:
\(sum \: of \: exterir \: anges \: for \: a \: polygon = 360 \\ 5x - 5 + x + 4x - 5 + 4x + 20 = 360 \\ x \: terms \: togather \\ 5x + x + 4x + 4x - 5 - 5 + 20 = 360 \\ 14x + 10 = 360 \\ 14x = 360 - 10 \\ 14x = 350 \\ x = \frac{350}{14} = 25 \\ x = 25 \\ thank \: you\)
Answer:
SUM OF EXTERIOR ANGLES=360
Step-by-step explanation:
5x-5+4x-5+4x+20+x=360
14x+10=360
14x=350
x=350/14
x=25